This paper examines the degree to which connectivity and automation can potentially reduce the overall fuel consumption of on-road vehicles. The paper begins with a simulation study highlighting the tradeoff between: (i) the fuel that a vehicle can save through speed trajectory shaping, versus (ii) the additional inter-vehicle spacing needed for this trajectory shaping to be feasible. This study shows that connectivity and automation are essential, rather than merely useful, for substantial reductions in the fuel consumed by fixed on-road vehicle powertrain/chassis configurations in traffic. Motivated by this insight, we survey the literature on the fuel savings achievable through different connected/automated vehicle technologies. This includes optimal vehicle routing, eco-arrival/departure at intersections, platooning, speed trajectory optimization, predictive driveline disengagement, predictive gear shifting, and predictive powertrain accessory control. This survey shows that the ability to shape vehicle speed trajectories collaboratively plays a dominant role in reducing urban/suburban fuel consumption, while platooning plays a dominant role in influencing the attainable fuel savings on the highway. Moreover, the survey shows that the degree to which connectivity/automation can reduce on-road vehicle fuel consumption, in both urban/suburban and highway settings, depends critically on the integration of powertrain- and chassis-level control.